What is the solution for y^{''}-6y^'+45y=0,y(0)=4,y^'(0)=-6 ?

The solution for y^{''}-6y^'+45y=0,y(0)=4,y^'(0)=-6 is y=e^{3t}(4cos(6t)-3sin(6t))

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

y^{''}-6y^'+45y=0,y(0)=4,y^'(0)=-6

y^{^{''}} - 6 y^{^{'}} + 45 y = 0, y (0) = 4, y^{^{'}} (0) = - 6

y = e^{3 t} (4 cos (6 t) - 3 sin (6 t))

Solution steps

y^{''} (t) - 6 y^{'} (t) + 45 y = 0

Solve linear ODE:

y = e^{3 t} (4 cos (6 t) - 3 sin (6 t))

y = e^{3 t} (4 cos (6 t) - 3 sin (6 t))

24 y^{^{''}} + y^{^{'}} - 3 y = 0

x^{^{''}} - x^{^{'}} + 2 x = 0

20 y^{^{''}} + 80 y^{^{'}} + 100 y = 0

2 y^{^{''}} + 3 y - 2 y = 0

\frac{d ^{2} y}{d x ^{2}} - 10 \frac{d y}{d x} - 3 y = 0

What is the solution for y^{''}-6y^'+45y=0,y(0)=4,y^'(0)=-6 ?
The solution for y^{''}-6y^'+45y=0,y(0)=4,y^'(0)=-6 is y=e^{3t}(4cos(6t)-3sin(6t))